Gain insights into Python for scientific computing. Explore arrays, plotting, linear equations, and algorithms using NumPy, Matplotlib, SciPy. Delve into applying tools with practical exercises.

Dockerfile.tar.gz

Python3

If you're a scientist or an engineer interested in learning scientific computing, this is the place to start.

In this course, you'll learn to write your own useful code to perform impactful scientific computations. Along the way, your understanding will be tested with periodic quizzes and exercises.

Topics covered in this course include arrays, plotting, linear equations, symbolic computation, scientific algorithms, and random variables. You’ll also be exposed to popular Python packages like NumPy, Matplotlib, SciPy, and others. In the last part of the course, the application section will test your ability to recall and apply the tools you have studied into newly learned scientific concepts.

At the end of this course, you'll be equipped with the tools necessary for everyday scientific computation.

Python for Scientists and Engineers

# Introduction
Optimization, or finding the minima or maxima of a function, is an important field in mathematics. Common applications of optimization are the minimization of entities such as cost, risk, and error, or the maximization of productivity, efficiency, and profit.
 

The minimization function `fmin` finds the next local minimum starting from a user-provided initial position. `fmin` is part of the `scipy.optimize` module. 



# Finding local minima 

There are two minimum input arguments for `fmin`:
1. The function to minimize. 
2. The initial value where  we start our search for the minimum.
 

`fmin` returns the value of the independent variable for which the function is locally minimized. 

```python 3
fmin(func, x0)
```

> <img src="/api/collection/10370001/6066104977850368/page/4580102618742784/image/6441996354846720" width="35"> The search for the minimum is local, since the algorithm follows the local gradient.

Let’s find the minima of this function:


$$f(x)=sin(x) - 2e^{ -(x - 0.4)^2}$$

We will be using a plot of the function’s data to best represent it:


This lesson discusses how to find the minima of a curve. 

Introduction

Python Refresher

Arrays

Plotting

Systems of Linear Equations

Symbolic Computation

Scientific Algorithms

Random Variables

Applications

Conclusion

Appendix

Python for Scientists and Engineers Exam

Optimization

Introduction #

Finding local minima